/*! \page REGION_FLUCTUATIONDoc Calculate the pair distribution function 

Keyword: REGION_FLUCTUATION

\section description Description

We define the number operator on as site i for spin \f$ \sigma \f$ as 
\f$ n_{i,\sigma}= \sum_{j\in \sigma} \Theta(r_j) \f$, where j is summed over the electrons in the spin \f$ \sigma \f$.
This object calculates the joint probability distribution function  between all pairs of sites and spins, \f$ \rho( n_{i,\sigma},n_{j,\sigma} ) \f$.


\section example Example

<pre>
method { VMC 
  average { region_fluctuation maxn 5 }
}
include qwalk.sys
trialfunc { include qwalk.slater } 
</pre>

The output should be relatively straightforward. 
An partial example might be:
<pre>
Region fluctuation
nspin 2 maxn 4 nregion 4
Spin 0 0 Region 0 0
0.4946464646 0 0 0 0.01615676261 0 0 0 
0 0.4975757576 0 0 0 0.01598456742 0 0 
0 0 0.007777777778 0 0 0 0.0009851002585 0 
0 0 0 0 0 0 0 0 
Spin 0 0 Region 0 1
0.1092929293 0.3784848485 0.006868686869 0 0.006368048054 0.01559836928 0.0009651245803 0 
0.3921212121 0.1054545455 0 0 0.01500690092 0.006139674008 0 0 
0.007777777778 0 0 0 0.0009851002585 0 0 0 
0 0 0 0 0 0 0 0 
</pre>
Since maxn was 4 in this case, for each set of two spins and two regions, the probability density is represented by a 4x4 matrix.  Each row of numbers is a row of the matrix followed the estimated error bars for that row.

\section options Options

\subsection reqopt Required 

<table>
<tr><th>Option</th><th>Type</th><th>Description</th></tr>
</table>


\subsection optopt Optional

While these options are not strictly needed, there are many cases in which the user may want to change them.

<table>
<tr><th>Option</th><th>Type</th><th>Default</th><th>Description</th></tr>


<tr><td>MAXN</td><td>Integer</td>
<td>20</td>
<td> The maximum number of electrons you expect to see on any atom </td>
</tr>
</table>

\subsection expopt Experimental options

</table>

*/
